Nat Ram Garg

On two-dimensional elastic dislocations in a multilayered half-space

The two-dimensional problem of a long displacement dislocation in a multilayered half-space is studied. Both plane strain and antiplane strain cases are considered. The Thomson-Haskell matrix method is used to obtain the static field caused by the dislocation. The source is represented in terms of the jumps at the source level in the depth-dependent factors in the Fourier integral representation of the displacements and stresses due to the source in an infinite medium. Explicit expressions for the surface displacements due to dip-slip and strike-slip faults of arbitrary dip are obtained. The formulation developed is quite convenient for numerical computation.

Displacements and stresses at any point of a uniform half-space due to two-dimensional buried sources

Closed-form analytical expressions for the displacements and stresses at an arbitrary point of a homogeneous, isotropic perfectly elastic half-space caused by various two-dimensional buried sources are obtained. The method consists of first finding the integral expressions for the half-space from the corresponding expressions for an unbounded medium given by Singh and Garg via the traction-free boundary conditions at the surface, and then evaluating the integrals analytically. Since the results are given for arbitrary Poissons ratio, the correspondence principle can be used to obtain the quasi-static displacements and stresses when the half-space is viscoelastic.

Plane strain deformation of an orthotropic elastic medium using an eigenvalue approach

The analytic expressions for the displacements and stresses at any point of an infinite orthotropic elastic medium as a result of an inclined line load have been obtained. This plane strain problem has been solved by using eigenvalue approach and the use of matrix notation avoids unwieldy mathematical expressions. The technique developed in the present paper is simple, straightforward and convenient for numerical computation. The variations of the displacements and stresses with the horizontal distance have been shown graphically.

Two-dimensional deformation of an orthotropic elastic medium due to seismic sources

Abstract The integral representation of two-dimensional seismic sources causing the antiplane strain deformation of an orthotropic elastic infinite medium has been obtained. Using this integral representation, the analytical expressions for the deformation of an orthotropic layered elastic medium due to a very long inclined strike-slip fault have been calculated, where the interface is horizontal and parallel to one plane of elastic symmetry. These expressions have been used to study the effect of the source location, dip of the fault and anisotropy of the medium on the horizontal displacement parallel to the fault. The variation of the horizontal displacement with the distance from the inclined fault is studied for three source locations: a surface-breaking fault and two buried faults. Both the source location and the dip of the fault are found to influence significantly the horizontal displacement at any point of an orthotropic elastic medium. Further, the horizontal displacement of an orthotropic elastic layered medium may differ significantly from that of an isotropic elastic layered medium.

Displacements and stresses in two welded half-spaces caused by two-dimensional sources

Closed-form analytic expressions for the displacements and stresses at any point of either of two homogeneous, isotropic, perfectly elastic half-spaces in welded contact caused by various two-dimensional sources are obtained. The method consists of first finding the integral expressions for two half-spaces in welded contact from the corresponding expressions for an unbounded medium by applying suitable boundary conditions at the interface and then evaluating the integrals analytically. The case of a long dip-slip dislocation source is considered in detail. Graphs showing the variation of the displacements with the distance from the fault and with the distance from the interface (depth) for a vertical dip-slip fault are presented. It is found that, although at a large distance from the fault, the variation with depth is smooth, at short distances the variation with depth is complex, with sharp maxima and minima.

Response of an anisotropic liquid-saturated porous medium due to two dimensional sources

Eigenvalue approach, following Laplace and Fourier transforms, has been employed to find the general solution to the field equations in an anisotropic liquid-saturated porous medium, in the transformed domain. The results of isotropic liquid-saturated porous medium can be derived as a special case. A numerical inversion technique has been applied to get the solutions in the physical domain. To illustrate the utility of the approach, an application of infinite space with impulsive force at the origin has been considered. The results in the form of displacement and stress components have been obtained and discussed graphically for a particular model.

Elastodynamics of an axisymmetric problem in an anisotropic liquid-saturated porous medium

The Laplace and Hankel transforms have been employed to find the general solution to the field equations in an anisotropic liquid-saturated porous medium for plain axisymmetric problem, in the transformed form. An application of an infinite space with impulsive force at the origin has been considered to show the utility of the solution obtained. The results of the corresponding problem in isotropic liquid-saturated porous medium can be derived as a special case. To get the solutions in the physical form, a numerical inversion technique has been applied. The results in the form of displacement and stress components have been obtained, numerically and discussed graphically for a particular model.

Two-dimensional static deformation of an anisotropic medium

The problem of two-dimensional static deformation of a monoclinic elastic medium has been studied using the eigenvalue method, following a Fourier transform. We have obtained expressions for displacements and stresses for the medium in the transformed domain. As an application of the above theory, the particular case of a normal line-load acting inside an orthotropic elastic half-space has been considered in detail and closed form expressions for the displacements and stresses are obtained. Further, the results for the displacements for a transversely isotropic as well as for an isotropic medium have also been derived in the closed form. The use of matrix notation is straightforward and avoids unwieldy mathematical expressions. To examine the effect of anisotropy, variations of dimensionless displacements for an orthotropic, transversely isotropic and isotropic elastic medium have been compared numerically and it is found that anisotropy affects the deformation significantly.

Static deformation of an orthotropic multilayered elastic half-space by two-dimensional surface loads

The transfer matrix approach is used to solve the problem of static deformation of an orthotropic multilayered elastic half-space by two-dimensional surface loads. The general problem is decoupled into two independent problems. The antiplane strain problem and the plane strain problem are considered in detail. Integral expressions for displacements and stresses at any point of the medium due to a normal line load and a shear line load, acting parallel to a symmetry axis, are obtained. In the case of a uniform half-space, closed form analytic expressions for displacements and stresses are derived. The procedure developed is quite easy and convenient for numerical computations.

Dynamic behaviour of an anisotropic liquid-saturated porous medium in frequency domain

A general solution to the field equations of an anisotropic liquid-saturated porous medium has been obtained, in the transformed form, using the Fourier transform. Assuming the disturbances to be harmonically time dependent, the transformed solution is obtained in the frequency domain. An application of a time-harmonic concentrated force acting at some interior point of an infinite medium has been considered to show the utility of the solution obtained. The transformed solutions are inverted numerically, using a numerical inversion technique to invert the Fourier transform. The results in the form of stress components have been obtained numerically and discussed graphically for a particular model. The results of the corresponding problem in isotropic liquid-saturated porous medium can be derived as a special case.